Stand with wonder on a mountaintop and enjoy the patterns of the scenery below - the fields and streams and hills and valleys and pathways; humans make some of those patterns, but it’s mostly natural. Look up in awe on a clear, starlit night and recognize the eternal beauty of the infinite universe; the patterns are there. Look inside yourself, at the patterns of your body as the lifeblood circulates through every tiny nook and cranny, and your lungs rhythmically breathe the air that surrounds you. Look deeper, and marvel at the simple symmetry of your DNA, as it splits and splits again, continuously making perfect copies of your very own ingredients.

Since the time of Galileo and Newton, formulas described everything, from the motion of tiny particles to planets in orbit, almost completely. Note the qualifier “almost completely” - therein lies the rub. The small shifts and perturbations were initially thought to be errors of measurement, and then later attributed to lesser known effects and/or more complicated formulas. And a continued procession of eminent theoreticians kept looking for the successive intricacies and nth degree effects to insert into the formulas. Mathematics was applied first to physical phenomena, sub-atomic particles and the orbits of distant stars; few bothered to find the formulas that predicted the patterns of seashells or spots on zebras.

Along came chaos theory (a misnomer for complexity science) that sparked interest in fractals - weird and beautiful shapes, complex geometric patterns with a series of identical, smaller shapes nested endlessly within, generated on computer screens using relatively simple rules. Fractals turn out pictures of featherlike fronds of fern composed of rows of smaller fronds, and the smaller fronds have their rows of even smaller fronds, in an endless pattern of beauty and simplicity.

Trees branching, rivers meandering, clouds puffs made of puffs, lightning zigzagging within lightning, insects whirring and birds wheeling in the sky, flames leaping, wind whispering through wheat fields, sand grains in aggregates clumping together, metal fracturing, earthquakes rending - all trace fractal paths through space and time. Processes in lungs, bowels and kidneys, in the neural networks of the brain, in the placenta and the heart, cones and rods in the eye, branching nerves - all are full of fractals, the perennial patterns of life.

For a long time fractals, and the allied area of cellular automata (CA), were relegated to the realm of computer geek's curiosity. The field of CA poses a spread-sheet-like universe in which individual cells move from one condition to another one click at a time, according to the rules that have been set (for example, a cell is black if one of its neighbors is black). The rules determine the color of each cell in the next iteration, and the pattern advances automatically.

CA was the brainchild of legendary mathematician John von Neumann who was interested in the idea of artificial life, particularly self-reproduction. He insisted that CA should not be seen solely as a mathematical abstraction, but as an analogy of the universe itself, where the patterns could actually stand for the mechanisms in the physical world. Perhaps the universe itself was a giant cellular automaton.

The intellectually arrogant Stephen Wolfram regards the early work with cellular automata as rudimentary. In his self-published, new book "A New Kind of Science", he uses no references from the numerous people who have contributed to the science over the years, perhaps considering their work irrelevant. Obsessed with the idea that he was on to something special, he spent more than a decade in isolation, pondering the possibilities and came up with this new tome - a telephone-book sized best-seller.

Wolfram insists that the universe can best be understood by grinding out results from simple rules. His big idea is that the algorithm is more basic and powerful than any mathematical equation. Not satisfied with simply explaining and justifying his contentions, he makes substantial efforts to apply his insights to dozens of fields.

Wolfram defines randomness, explains seeming randomness in financial markets, finds an exception to the second law of thermodynamics, conjectures why extraterrestrials might be communicating with us in messages we can't perceive, elaborates on why humans appear to have free will, reconstructs the foundations of mathematics, devises a new way to perform encryption, insists that Darwinian natural selection is an overrated component in evolution.

After hundreds of pages of laying groundwork, presenting case after case of visual examples where simple rules generate counter-intuitively complex results, Wolfram concludes that the phenomenon of rule-based complexity is overwhelmingly commonplace - it’s at the basis of everything.

Wolfram goes further, stating that once a system achieves a certain, easily attainable degree of complexity, it has reached the point of maximum complexity, as measured by the computation required to crank out the end result. Everything at that level of complexity - and that includes almost everything, from human thought to ocean waves on the seashore - is exactly as complex as anything else.

Wolfram theorizes that there's an ultimate model for the universe, the mother of all rules; a single, simple "ultimate rule" that computes everything. The climax of the book is the principle of computational equivalence, which might be called "Wolfram's law."

Ultimately, Wolfram believes that his methods will generate rules that create phenomena identical to everything found in the natural world. The start of this excitement is the demonstration of rules that seem to produce on a computer the same results as pigmentation patterns on jaguars and seashells, the growth of leaves, the behavior of financial markets. <:> Wolfram offers no deterministic proof - just demonstrations and contentions. I feel intuitively that this approach is right. The only question is - did Wolfram "discover" it?